At a festive, daddy-daughter bash on Father’s Day, Jason Terry delivered some tough news for Mavericks fans to hear.

If the 2011 NBA champions elect to rebuild their team with one-year contract “rentals,” Terry will be playing elsewhere next season.

Terry, whose six-year, $57 million contract ends on July 1, when he becomes an unrestricted free agent, said Sunday he wants to sign another multiyear deal, preferably with the Mavericks. But as the Mavericks’ free-agent possibilities start to take shape, it won’t happen for one year.

“It’s a tough situation,” Terry said. “I’m finally in a position where I can kind of predict my own future, so to speak. I want to stay here in Dallas. That’s always been my goal. But it needs to be long-term. If they’re not ready to step up and do that, then I’ll have to make my home elsewhere.”

This may be yet another reason fans should want the Mavericks to hit a home run in the Deron Williams Derby. If they don’t get the top free agent on the market this season, they may elect to hire players willing to play on one-year contracts and keep their free-agent money available for next summer, when Dwight Howard and Chris Paul headline the free-agent class.

“I won’t be here,” Terry said if the Mavericks take that route. “You can count on that. If they’re doing that, you won’t see the Jet on the runway in Dallas. But my time here was good.”

Terry was on the open market for barely 12 hours in 2006, when he signed his last free-agent deal. He would like to have another fast conclusion but wants to make the right decision, even if it’s not quick.

Terry also changed agents, dropping Dan Fegan and hiring Arn Tellem and B.J. Armstrong from the Wasserman Group. It’s been quiet on the free-agent front because teams are not allowed to contact players or agents until July 1.

No matter where free agency takes him, Terry said his time in Dallas probably is not done.

“Down the road as a player or in some capacity within the organization,” he said. “Obviously, my foundation will remain active in Dallas. And for me, coming back and working for the organization in one position or another has been discussed, and [owner Mark] Cuban and I are on the same page.”

“And even if I’m playing somewhere else, everything we accomplished here will not be for naught — winning a championship, revitalizing my career here coming from Atlanta. Coming here has been all I thought it would be.”

Terry recently returned from China for several functions, including an NBA Cares outing. On Sunday, he had his Daddy-Daughter charity event for the Jason Terry Foundation at the Crescent Hotel. The lineup of dads included owner Mark Cuban, coach Rick Carlisle, Emmitt Smith and many others — plus their daughters.

“This is cool. This is one of the joys of being a father,” Terry said. “Usually on Father’s Day, everybody honors us; this is more something for us to honor our daughters. Obviously, the father-daughter relationship is one that’s very fragile, delicate and very special to all us fathers.”

The Celtics are preparing themselves for the possible loss of Allen, and began the process of recruiting Terry after midnight ET Saturday, league sources said.

The Mavericks still have interest in re-signing Terry. The Los Angeles Clippers also have emerged as suitors, sources said. The Celtics also have interest in Los Angeles Clippers free agent guard Nick Young, sources said.